# What is Logic?

 Necessity and Contingency To understand logic it is first necessary to grasp the important distinction between contingent propositions, which might or might not be true, and necessary propositions, which could not be false. support for the distinction against the distinction Logic is the study of necessary truths and of systematic methods for clearly expressing and rigorously demonstrating such truths. why this definition? other definitions Logic and Analytic Philosophy Because the methods of analytic philosophy are mainly a priori philosophy is concerned with logic not only as a subject matter but as an important contribution to the methods of philosophy. Analytic Philosophy IS Logic Analytic Philosophy IS NOT Logic

## Necessity and Contingency:

 As a prelude to defining logic we try to clarify the meaning of necessity by contrast with its opposite contingency.
 Carts and Horses A few words about why it may be thought desirable to draw the necessary/contingent line, and to get it in the right place. The Fundamental Triple-Dichotomy "necessary" and "contingent" together form one of three dichotomies which have often been thought very closely related.
 Some Necessary Propositions Four examples of necessary propositions which help to illustrate some of the issues involved in getting the line in the right place.
 Definitions of Necessary and Contingent We discuss three different kinds of necessity related to the examples of necessary propositions. Possible Worlds To get a sharper grip on necessity we go via possibility, looking at what it takes to make a possible world.

## Why this Definition?:

 A key feature of logic is that it is concerned with sound, a priori arguments, viz. those in which conclusions follow of necessity. The proposed definition seeks to make direct the connection between logic and necessity.
 Criteria for Definition Two criteria for adequacy of a definition of logic are: that it can be explained as clearly as possible that it correctly delineates the sphere in which logical methods are applicable
 Clarity It remains to be seen how clear this definition can be rendered. It doesn't take us very far. We will supply a definition of necessary truth in terms of possible worlds, which I hope will help.
 The Sphere of Logic The intention is to put forward a definition of logic which makes logic encompass all sound a priori reasoning. It is my belief that the more common definitions of logic fail to do this. In particular, we seek a defensible definition of logic within which the truths of mathematics can be seen to fall.

## Other Definitions:

 Some ways of defining "Logic" are introduced and their merits discussed.
 Introduction A bit of preliminary discussion about what we are looking for here. Evaluation Criteria How do we know when we have a good definition? Here are some criteria which we can use to assess candidates. methods, systems, truths are all involved, a definition can be approached through any one methods Logic can be defined as concerned with methods for reasoning. Logical systems are then formalisations of the proper methods and logical truths are those demonstrable by correct methods. systems logic can be defined as concerned with a certain class of logical systems, logical truths would then be defined in terms of their derivibility in the systems. truths Here certain kinds of truths are the definitive concern, systems and methods are then judged in terms of their ability to confirm this kind of truth.

## Analytic Philosophy IS Logic:

 That philosophers derive truths by reason rather than experiment encourages many to believe that their conclusions have the force of logic, and others to deny the legitimacy of philosophical conclusions which are not analytic.
 Rationalists Rationalist philosophers can perhaps be regarded as subscribing to the view that philosophy (sometimes in a very broad sense) derives conclusions by deductive methods and that in consequence these conclusions may be considered a part of logic. In practice their conclusions have rarely been logical truths, and we may debate whether this is because they in fact believed philosophy to go beyond logic or because they had a defective understanding of the limits of logic (and hence of philosophy also).
 Atomism The heyday for logic in philosophy was the early decades of this century after the success of Frege and Russell in (mostly) formalising mathematics using logic. Atomism sought to re-build philosophical doctrine in the light of the logical advances, but thought perhaps too little about the status of philosophy itself to be credited with the identification of philosophy and logic. Nevertheless the point that philosophy is indistinguishable from logic is made by Bertrand Russell in 1914.
 Positivism The Logical positivists did give a great deal of attention to the status of philosophy. Like Russell before him, A.J.Ayer explicitly affirmed that philosophy is a department of logic. Rudolf Carnap's account of the syntactic method practised by the Vienna Circle advocates the method of semantic ascent as a way of making explicit the linguistic, and hence logical, character of philosophical propositions which might otherwise appear to be concerned with matters of fact.

## Analytic Philosophy IS NOT Logic:

 Analytic philosophers, even the most ardent proponents of logic, have never confined themselves to enunciating logical truths. Furthermore, not all truths about language are truths of logic.
 Origins of Analytic Philosophy The modern origin of "analytic" philosophy is popularly located with Russell and Moore. Russell's analytic bent was to formal logical analysis, and this tendency leads us first to logical atomism and then to logical positivism, neither of which provides a satisfactory account of how logic can subsume philosophy. Moore was a common sense philosopher, and this tendency, mediated by Ludwig Wittgenstein had an impact on the practice of philosophy far greater than that of atomism or positivism. The kind of analysis involved here, the analysis of ordinary language, is very far removed from logical analysis, and exposes (as it were, by caricature) a weakness in the positivist account of analysis.
 Analysis of Language Carnap believed that since an analytic truth owes its truth to features of language it must be equivalent to a statement about language, and possibly also that true statements about language are likely to be analytic. Both of these views are incorrect, and it is this which has enabled philosophers to engage in analysis of language without confining themselves to logic. Statements about languages are only potentially analytic if the language in question has been formally defined, so that the statements can be logically derived from the definitions. In the case of natural languages it is doubtful that formal definitions, or even precise informal ones, will ever be available.

## Logic and Analytic Philosophy:

 Whatever we think about where demarcation lines should be drawn, there remains some interest in the question "how might analytic philosophy contribute to or benefit from logical analysis?".
 History: varieties of 20thC philosophical analysis are contrasted with the formal analysis advocated here Epistemology: familiar fundamental epistemological distinctions are identified on which formal analysis is predicated
 Logic: an analysis of the nature of logical truth leads to firm logical foundations for formal analysis Mathematics: the logicist thesis is re-affirmed and related to other positions in mathematical philosophy
 Engineering: a formal analytic position is elaborated on the application of logic through mathematics in science and engineering Philosophy: applications of formal analysis in philosophy are considered